The present invention relates to a filter and, more particularly, to an active filter including passive filter elements.
Generally, active filters are known for their simple adjustment. Their central frequency f.sub.0 can be adjusted independently of selectivity Q, while their selectivity Q can be adjusted independently of central frequency f.sub.0. Furthermore, the active filters are known for their long life and can be arranged in an integrated circuit.
The most commonly used and popular active filter is a biquad active filter which is shown in FIG. 1. The biquad active filter includes a differential amplifier P1 formed by an operational amplifier. The amplifier P1 has inverting and non-inverting inputs and an output. The inverting input of the amplifier P1 is connected through a resistor R1 to an input terminal of the active filter and the non-inverting input of the same is connected to the ground. The output of the amplifier P1 is connected to an output terminal of the active filters. A resistor R2 and a capacitor C1 are connected in parallel between the inverting input and the output of the amplifier P1. The biquad active filter also includes a second differential amplifier P2 formed by an operational amplifier in which the inverting input thereof is connected through a resistor R3 to the output of the amplifier P1 and the non-inverting thereof is grounded. A resistor R4 is connected between the output and inverting input of the second operational amplifier P2. The biquad active filter further includes a third differential amplifier P3 also formed by an operational amplifier in which the inverting input thereof is connected through a resistor R5 to the output of the second operational amplifier P2 and the non-inverting input thereof is connected to the ground. A capacitor C2 is connected between the output and inverting input of the amplifier P3. The output of the amplifier P3 is fed back to the inverting input of the first amplifier P1 through a resistor R6.
The reference characters for the resistors and capacitors described above and below represents the respective capacitance and resistance.
The transfer function T'(s) of the biquad active filter can be expressed as follows: ##EQU1## in which V1' and V2' are signal levels at the input and output terminals of the biquad active filter, respectively, K is R4/R3 and s is a product of conjugate j multiplied by 2.pi.f.sub.0.
The central frequency f.sub.0 ' and 3dB bandwidth .DELTA.f' can be expressed as follows: ##EQU2## From equations (2) and (3), it is understood that the central frequency f.sub.0 ' can be adjusted by changing the values of C2, R5 and R6 without interrupting the 3dB bandwidth .DELTA.f' and that the 3dB bandwidth .DELTA.f' can be adjusted by changing the value of R2 without interrupting the central frequency f.sub.0 '. Since the selectivity Q' can be expressed as Q'=f.sub.0 '/.DELTA.f', the selectivity Q' can be adjusted by the change of 3dB bandwidth .DELTA.f'. The equations (1), (2) and (3) are well known, so a further description is omitted.
The above described biquad active filter requires at least three differential amplifiers.
Accordingly, a primary object of the present invention is to provide an active filter which requires only two differential amplifiers and yet functions exactly the same as the conventional biquad active filter.